I'm a granny of a 3 1/2 yo grandboy, and I share your concern about butting in and the risk of annoying or insulting my daughter and son-in-law. Cooperation and consistency among caregivers are important values.
BUT, if I were experiencing this conundrum, I'd be inclined to buy a potty chair (maybe from a thrift shop), and a box of pull-ups that the little girl can pull down herself when the urge hits. I wouldn't make a big deal of it, but if my daughter asked why I did it, I'd just say I wanted to experiment a bit to find out what works best at my house. And it may be only a temporary situation as your granddaughter gets more used to the whole challenge of potty training.
That's quite different, I think, from butting in - your relationship, patterns and techniques with your grandgirl are not an identical copy of her mother's. Nor should you expect them to be. You bring unique and valuable differences into this little girl's life, and children can benefit immensely from this richness if it is thoughtful and loving, and shares common goals with their parents.
So, if and when the subject arises, express your need to find the solution that works best for you in a happy, matter-of-fact tone, and ask your daughter whether she has any problem with your approach. If she says yes, ask her to explain, and listen closely. She may have a good point that you can honor. Or she may discover she doesn't have a good reason to object to the potty chair. Either way, she's not likely to fire you for trying, is she?
Good luck. I'd love to hear in a week or two "what happened."